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Electron nano-diffraction study of carbon single-walled nanotube ropes
7 February 1997
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 265 (1997) 379-384
Electron nano-diffraction study of carbon single-walled nanotube ropes J.M. Cowley a, Pavel Nikolaev h, Andreas Thess h, Richard E. Smalley h a Department of Physics and Astroru~my, Arizona State University, Tempe, AZ 85287-1504, USA b Center for Nanoscale Science and Technology, Rice Quantum Institute and Departments of Chemistry and Physics, MS-100, Rice University, P.O. Box 1892, Houston, TX 77251, USA Received 14 August 1996; in l'mal form 25 November 1996
Abstract
Electron diffraction patterns from regions about 0.7 nm in diameter have been obtained, in conjunction with dark-field imaging, in a scanning transmission electron microscope to study the average helicity and the local variations of helicity of the individual carbon nanotubes within the ropes of single-walled carbon nanotubes recently produced by double laser irradiation. It has been found that the predominant helicity is that predicted theoretically, namely that giving the metallic, Csv symmetry, (10,10) tube.
1. Introduction
In a recent publication [1], Thess et ai. report the characterization of ropes of single-walled carbon nanotubes (SWnT) by use of electron microscopy, X-ray diffraction and measurements of resistivity and electron spin resonance spectra. The ropes are formed by laser irradiation, followed by a second laser pulse. The individual nanotubes within the ropes, each consisting of single graphene sheets wrapped into a cylinder with a characteristic helix angle [2], are of remarkably uniform diameter, 1.36 nm, and are tens or hundreds of microns long. They are packed within the ropes in a two-dimensional hexagonal packing with van der Waals inter-tube bonding and lattice spacing 1.7 nm. The ropes are seen by transmission electron microscopy to be 5 to
20 nm in diameter and are usually bent, twisted and tangled in a disorderly array. A theoretical treatment of the growth mechanisms giving rise to such arrays of nanotubes [1,3], suggests that the energetically-favored form of the individual nanotubes should be that for which the C - C bonds are perpendicular to the axis of the tube, the 'arm-chair' configuration designated as (10,10) [4]. For convenience we will refer to this configuration as having 0 ° helicity. Since it is difficult to derive the helicity of the tubes by conventional electron microscopy or by X-ray diffraction (in the absence of any strongly-preferred alignment of the ropes), we have applied the methods of nanodiffraction available in a scanning transmission electron microscopy (STEM) instrument [5], which allow diffraction patterns to be
0009-2614/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S 0 0 0 9 - 2 6 1 4(96)01 4 4 2 - X
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J.M. Cowley et a l . / Chemical Physics Letters 265 (1997) 379-384
obtained from any region, 1 nm or less in diameter, selected from a bright-field or dark-field STEM image. The STEM instrument used is an HB-5 from VG Microscopes Ltd. modified by addition of a high-resolution objective lens pole-piece and a special detector system for recording diffraction patterns by use of a low-light-level TV camera and VCR system or a CCD camera with digital data-handling system [6]. For studying the nanotubes we used an electron beam of diameter 0.7 nm which was either held stationary at a chosen spot within the dark-field image of a rope or else was scanned rapidly over an area of the rope, 10-20 nm in diameter, during the recording time, in order to give an indication of the average structure of the nanotubes within the rope.
The diffraction pattern to be expected from a single-walled nanotube can be derived, in an adequate approximation, by forming the reciprocal-space distribution for a single flat graphitic carbon sheet (with continuous straight lines perpendicular to the sheet through the hk reciprocal lattice points) and rotating it about the tube axis, as suggested in Fig. 1, to give scattering power in a set of planes, falling away rapidly from sets of circles. The diffraction patterns are given by intersection of the Ewald sphere, considered planar, with this distribution of scattering power, and depend on the helicity (which gives a doubling of spots except for 0 or 30 ° helicities) and the tilt of the tube with respect to the incident beam (see also [7]). Fig. 2 suggests the form of the diffraction pattern for a tube with the 0 ° helicity and for
f
2,0
,r
/
1,I
x~"~\6
AXIS of TUBE
/
~k~ PlanarEwaldsphere
Fig. 1. The reciprocal-space distribution for a single-walled carbon nanotube, derived by constructing continuous straight lines through the h,k reciprocal lattice points for a single flat graphitic carbon sheet and rotating them about the tube axis. The intersection of the Ewald sphere, considered planar for high-energy electrons, with this distribution is indicated for tilt angles, ~b, of 0 and 30 ° of the tube axis.
J.M. Cowley et al. / Chemical Physics Letters 265 (1997) 379-384
¢=0
~=30
t
l,,, I
"~qlL~ °
',°
i a,-~
Fig. 2. Sketches of the electron diffraction patterns expected from the diagram of Fig. 1, for tilt angles of 0 and 30 °, for a (10,10) nanotube (helix angle 0 °)
tilts of the tube of 0 and 30 °, corresponding to the Ewald sphere orientations of Fig. 1. Fig. 3 suggests the passage of an electron beam through a rope of diameter about 12 nm so that the diffraction pattem is given by a number of SWnT. For a rope with all tubes having zero helicity, and 0 ° tilt, the diffraction pattern, apart from the equatorial line through the origin, shows the hexagonal arrays of (1,0) and (1,1) spots, as given by the individual tubes. The variation with tilt can be derived by considering Fig. 1. The strong equatorial line has an intensity distribution which is modulated by the lateral stacking of the SWnT in the hexagonal array, but this stacking has very little effect on the remainder of the pattern.
a strong preference for a helicity of 5° away from zero; 5 showed a spread of helix angles from 0 to about 5 ° (as indicated by the continuous arcing of the spots); 12 showed a spread of helix angles of up to about 10° (Fig. 4(d)), and 3 showed a well defined preference for a helix angle of about 10° (Fig. 4(c)). There was no obvious correlation between the values or spreads of helix angles and the rope diameters. For those ropes showing the presence of a range of helix angles of either 5 or 10°, the diffraction patterns taken at selected spot positions within the image of the rope showed the presence of several, but usually not more than two, different helix angles, as seen in Fig. 4(e) and (f). This, and the lack of symmetry of the intensities of the spots around the origin, strongly suggest that there are regions within the cross-sections of the ropes, which have a nearperfect hexagonal stacking of nanotubes with identical helix angles. These regions tend to constitute large fractions of the ropes, and so have diameters of the order of 10 nm or more in some cases. An interesting observation has been made that the dark-field STEM images of the ropes, obtained with a detector set to record diffraction spots correspond-
( 2. Observations Diffraction patterns, and corresponding images have been recorded for a total of 35 ropes. Regions of the ropes were selected to exclude those too obviously bent, twisted, tilted with respect to the beam or contaminated with amorphous or other extraneous material. The rope diameters varied from 3 to 30 nm. For all of these ropes except two, the predominant helicity, shown by the averaged diffraction patterns obtained with the beam scanned over the rope diameter, was around 0 °. For one narrow rope the helicity was 30 ° away from this, and for one rope there was a mixture of 30 and 0 ° helicities. Of the 33 ropes showing an average helicity of around 0 °, 9 showed an exact 0 ° helix angle with no appreciable spread of helicities (patterns such as in Fig. 4(a,b)); 4 showed
381
(
?
7
C( (
(
~7 I/1 ../i zll ill
/// //z l// /li ill iti /ll I/I III
eli
YA z/.. i1"/ // i/ l/ ,.i/
"/Z /f/ /// II/ Ill
e -
V Fig. 3. Cross-sectional diagram of a rope of SWnT, of diameter about 12 nm, with an electron beam passing through.
382
J.M. Cowley et al.// Chemical Physics Letters 265 (1997) 379-384
ing to spacings of about 0.3 to 0.7 rim, show bright bands and, frequently, sharp bright spots, as in Fig. 5. These bright spots did not show any clear correspondence with helix angles. E x a m i n a t i o n of the
intensity distributions along the strong equatorial line of scattering in the nanodiffraction patterns, however, indicated that the bright spots were associated with variations of the regularity and orientation of
Fig. 4. Nanodiffraction patterns from SWnT ropes. (a). Average pattern from 0° helix rope, 0° tilt. (c.f., Fig. 2(a)). (b) Ditto, with slightly more than 30° tilt (c.f. Fig. 2(b)). (c) Average pattern for 10° helix angle, zero tilt. (d,e,f) Average pattern and spot patterns for a spread of about 10° in helix angles.
J.M. Cowley et al./ Chemical Physics Letters 265 (1997) 379-384
383
structures, then it may be concluded that 44% of the nanotubes are (10,10), 30% are (11,9) and 20% are
(12.8).
Fig. 5. Dark-field STEM image of a SWnT rope showing bright spots and streaks. Marker= 10 nm.
the stacking of the individual nanotubes within the ropes.
3. Discussion, conclusions The observations of nanodiffraction patterns show general agreement with the theoretical predictions that the 0 ° helix angle, the (10,10) configuration, should be energetically favored and should occur most frequently. The helix angles of about 5 and 10°, which are also found with relatively high probability may well correspond to the (11,9) and (12,8) configurations, for which the helix angles differ from the (10,10) by 5 and 9.5 °, respectively. The nanotube diameters for these configurations are expected to differ from those for the (10,10) by less than 1 percent, and these configurations are expected to be favored energetically more than any other configuration except the (10,10) [3]. If it is assumed that the ropes showing an average pattern with a spread of up to 5° consist of an equal mixture of (10,10) and (11,9) and those ropes showing a spread of about 10° consist of equal parts of (10,10), (11,9) and (12,8)
The spot nanodiffraction patterns, obtained with the incident beam held stationary at a chosen part of the STEM image, show clearly that, even when a spread of helix angles exists in the rope, a line drawn through the rope in the beam direction rarely intersects more than two regions of different helix angle. Hence there is a strong tendency for the formation of hexagonal close-packed arrays of nanotubes which all have the same diameter and helix angle. It may be suggested that, in the process of formation of the ropes, the initial formation is of ropes of nanotubes (up to about 10 nm in diameter) which are uniform in nanotube diameter and helix angle, and then such ropes aggregate with others which may or may not have the same chirality. An analysis of the bright bands and streaky spots which appear in the dark-field images of the ropes has been made by observing the series of nanodiffraction patterns obtained as the incident beam is scanned slowly across the image of a rope. These results will be reported elsewhere, but it may be stated here that the image contrast may be interpreted in terms of the twisting and bending of the ropes and the occurrence of local defects in the lateral stacking of the nanotubes. Such defects may be associated with the changes of helix angle implied above or possibly with other types of modification of tube structure, or with inclusions or stacking faults.
Acknowledgements This research was supported by the Office of Naval Research (grant N0014-91-J1794 and order number N0014-95-F-0099), the Advanced Technology Program of the State of Texas (grant 003604-047) and the Robert A. Welch Foundation, and made use of the instrumentation of the Center for High Resolution Electron Microscopy at Arizona State University.
References [I] A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Pelit, J. Robert, C. Xu, Y.H. Lee, S.G. Kim, D.T. Colbert, G. Scuseria, D.
384
J.M. Cowley et aL / Chemical Physics Letters 265 (1997) 379-384
Tom{reek, J.R. Fischer and R.E. Smalley, Science 273 (1996) 483. [2] S. lijima and T. Ichihashi, Nature 363 (1993) 603. [3] C. Xu, D.T. Colbert, R.E. Smalley and G.E. Scuseria. in preparation. [4] N. Hamada, S. Sawada and A. Oshiyama, Phys. Rev. Lett., 68 (1992) 1579.
[5] J.M. Cowley, J. Electron Microsc. 45 (1996) 3. [6] J.M. Cowley, Ultramicroscopy 49 (1993) 4. [7] X.B. Zhang, X.F. Zhang, S. Amelinckx, G. Van Tenderloo, J Van Landuyt, Ultramicroscopy, 54 (1994) 237.
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 265 (1997) 379-384
Electron nano-diffraction study of carbon single-walled nanotube ropes J.M. Cowley a, Pavel Nikolaev h, Andreas Thess h, Richard E. Smalley h a Department of Physics and Astroru~my, Arizona State University, Tempe, AZ 85287-1504, USA b Center for Nanoscale Science and Technology, Rice Quantum Institute and Departments of Chemistry and Physics, MS-100, Rice University, P.O. Box 1892, Houston, TX 77251, USA Received 14 August 1996; in l'mal form 25 November 1996
Abstract
Electron diffraction patterns from regions about 0.7 nm in diameter have been obtained, in conjunction with dark-field imaging, in a scanning transmission electron microscope to study the average helicity and the local variations of helicity of the individual carbon nanotubes within the ropes of single-walled carbon nanotubes recently produced by double laser irradiation. It has been found that the predominant helicity is that predicted theoretically, namely that giving the metallic, Csv symmetry, (10,10) tube.
1. Introduction
In a recent publication [1], Thess et ai. report the characterization of ropes of single-walled carbon nanotubes (SWnT) by use of electron microscopy, X-ray diffraction and measurements of resistivity and electron spin resonance spectra. The ropes are formed by laser irradiation, followed by a second laser pulse. The individual nanotubes within the ropes, each consisting of single graphene sheets wrapped into a cylinder with a characteristic helix angle [2], are of remarkably uniform diameter, 1.36 nm, and are tens or hundreds of microns long. They are packed within the ropes in a two-dimensional hexagonal packing with van der Waals inter-tube bonding and lattice spacing 1.7 nm. The ropes are seen by transmission electron microscopy to be 5 to
20 nm in diameter and are usually bent, twisted and tangled in a disorderly array. A theoretical treatment of the growth mechanisms giving rise to such arrays of nanotubes [1,3], suggests that the energetically-favored form of the individual nanotubes should be that for which the C - C bonds are perpendicular to the axis of the tube, the 'arm-chair' configuration designated as (10,10) [4]. For convenience we will refer to this configuration as having 0 ° helicity. Since it is difficult to derive the helicity of the tubes by conventional electron microscopy or by X-ray diffraction (in the absence of any strongly-preferred alignment of the ropes), we have applied the methods of nanodiffraction available in a scanning transmission electron microscopy (STEM) instrument [5], which allow diffraction patterns to be
0009-2614/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S 0 0 0 9 - 2 6 1 4(96)01 4 4 2 - X
380
J.M. Cowley et a l . / Chemical Physics Letters 265 (1997) 379-384
obtained from any region, 1 nm or less in diameter, selected from a bright-field or dark-field STEM image. The STEM instrument used is an HB-5 from VG Microscopes Ltd. modified by addition of a high-resolution objective lens pole-piece and a special detector system for recording diffraction patterns by use of a low-light-level TV camera and VCR system or a CCD camera with digital data-handling system [6]. For studying the nanotubes we used an electron beam of diameter 0.7 nm which was either held stationary at a chosen spot within the dark-field image of a rope or else was scanned rapidly over an area of the rope, 10-20 nm in diameter, during the recording time, in order to give an indication of the average structure of the nanotubes within the rope.
The diffraction pattern to be expected from a single-walled nanotube can be derived, in an adequate approximation, by forming the reciprocal-space distribution for a single flat graphitic carbon sheet (with continuous straight lines perpendicular to the sheet through the hk reciprocal lattice points) and rotating it about the tube axis, as suggested in Fig. 1, to give scattering power in a set of planes, falling away rapidly from sets of circles. The diffraction patterns are given by intersection of the Ewald sphere, considered planar, with this distribution of scattering power, and depend on the helicity (which gives a doubling of spots except for 0 or 30 ° helicities) and the tilt of the tube with respect to the incident beam (see also [7]). Fig. 2 suggests the form of the diffraction pattern for a tube with the 0 ° helicity and for
f
2,0
,r
/
1,I
x~"~\6
AXIS of TUBE
/
~k~ PlanarEwaldsphere
Fig. 1. The reciprocal-space distribution for a single-walled carbon nanotube, derived by constructing continuous straight lines through the h,k reciprocal lattice points for a single flat graphitic carbon sheet and rotating them about the tube axis. The intersection of the Ewald sphere, considered planar for high-energy electrons, with this distribution is indicated for tilt angles, ~b, of 0 and 30 ° of the tube axis.
J.M. Cowley et al. / Chemical Physics Letters 265 (1997) 379-384
¢=0
~=30
t
l,,, I
"~qlL~ °
',°
i a,-~
Fig. 2. Sketches of the electron diffraction patterns expected from the diagram of Fig. 1, for tilt angles of 0 and 30 °, for a (10,10) nanotube (helix angle 0 °)
tilts of the tube of 0 and 30 °, corresponding to the Ewald sphere orientations of Fig. 1. Fig. 3 suggests the passage of an electron beam through a rope of diameter about 12 nm so that the diffraction pattem is given by a number of SWnT. For a rope with all tubes having zero helicity, and 0 ° tilt, the diffraction pattern, apart from the equatorial line through the origin, shows the hexagonal arrays of (1,0) and (1,1) spots, as given by the individual tubes. The variation with tilt can be derived by considering Fig. 1. The strong equatorial line has an intensity distribution which is modulated by the lateral stacking of the SWnT in the hexagonal array, but this stacking has very little effect on the remainder of the pattern.
a strong preference for a helicity of 5° away from zero; 5 showed a spread of helix angles from 0 to about 5 ° (as indicated by the continuous arcing of the spots); 12 showed a spread of helix angles of up to about 10° (Fig. 4(d)), and 3 showed a well defined preference for a helix angle of about 10° (Fig. 4(c)). There was no obvious correlation between the values or spreads of helix angles and the rope diameters. For those ropes showing the presence of a range of helix angles of either 5 or 10°, the diffraction patterns taken at selected spot positions within the image of the rope showed the presence of several, but usually not more than two, different helix angles, as seen in Fig. 4(e) and (f). This, and the lack of symmetry of the intensities of the spots around the origin, strongly suggest that there are regions within the cross-sections of the ropes, which have a nearperfect hexagonal stacking of nanotubes with identical helix angles. These regions tend to constitute large fractions of the ropes, and so have diameters of the order of 10 nm or more in some cases. An interesting observation has been made that the dark-field STEM images of the ropes, obtained with a detector set to record diffraction spots correspond-
( 2. Observations Diffraction patterns, and corresponding images have been recorded for a total of 35 ropes. Regions of the ropes were selected to exclude those too obviously bent, twisted, tilted with respect to the beam or contaminated with amorphous or other extraneous material. The rope diameters varied from 3 to 30 nm. For all of these ropes except two, the predominant helicity, shown by the averaged diffraction patterns obtained with the beam scanned over the rope diameter, was around 0 °. For one narrow rope the helicity was 30 ° away from this, and for one rope there was a mixture of 30 and 0 ° helicities. Of the 33 ropes showing an average helicity of around 0 °, 9 showed an exact 0 ° helix angle with no appreciable spread of helicities (patterns such as in Fig. 4(a,b)); 4 showed
381
(
?
7
C( (
(
~7 I/1 ../i zll ill
/// //z l// /li ill iti /ll I/I III
eli
YA z/.. i1"/ // i/ l/ ,.i/
"/Z /f/ /// II/ Ill
e -
V Fig. 3. Cross-sectional diagram of a rope of SWnT, of diameter about 12 nm, with an electron beam passing through.
382
J.M. Cowley et al.// Chemical Physics Letters 265 (1997) 379-384
ing to spacings of about 0.3 to 0.7 rim, show bright bands and, frequently, sharp bright spots, as in Fig. 5. These bright spots did not show any clear correspondence with helix angles. E x a m i n a t i o n of the
intensity distributions along the strong equatorial line of scattering in the nanodiffraction patterns, however, indicated that the bright spots were associated with variations of the regularity and orientation of
Fig. 4. Nanodiffraction patterns from SWnT ropes. (a). Average pattern from 0° helix rope, 0° tilt. (c.f., Fig. 2(a)). (b) Ditto, with slightly more than 30° tilt (c.f. Fig. 2(b)). (c) Average pattern for 10° helix angle, zero tilt. (d,e,f) Average pattern and spot patterns for a spread of about 10° in helix angles.
J.M. Cowley et al./ Chemical Physics Letters 265 (1997) 379-384
383
structures, then it may be concluded that 44% of the nanotubes are (10,10), 30% are (11,9) and 20% are
(12.8).
Fig. 5. Dark-field STEM image of a SWnT rope showing bright spots and streaks. Marker= 10 nm.
the stacking of the individual nanotubes within the ropes.
3. Discussion, conclusions The observations of nanodiffraction patterns show general agreement with the theoretical predictions that the 0 ° helix angle, the (10,10) configuration, should be energetically favored and should occur most frequently. The helix angles of about 5 and 10°, which are also found with relatively high probability may well correspond to the (11,9) and (12,8) configurations, for which the helix angles differ from the (10,10) by 5 and 9.5 °, respectively. The nanotube diameters for these configurations are expected to differ from those for the (10,10) by less than 1 percent, and these configurations are expected to be favored energetically more than any other configuration except the (10,10) [3]. If it is assumed that the ropes showing an average pattern with a spread of up to 5° consist of an equal mixture of (10,10) and (11,9) and those ropes showing a spread of about 10° consist of equal parts of (10,10), (11,9) and (12,8)
The spot nanodiffraction patterns, obtained with the incident beam held stationary at a chosen part of the STEM image, show clearly that, even when a spread of helix angles exists in the rope, a line drawn through the rope in the beam direction rarely intersects more than two regions of different helix angle. Hence there is a strong tendency for the formation of hexagonal close-packed arrays of nanotubes which all have the same diameter and helix angle. It may be suggested that, in the process of formation of the ropes, the initial formation is of ropes of nanotubes (up to about 10 nm in diameter) which are uniform in nanotube diameter and helix angle, and then such ropes aggregate with others which may or may not have the same chirality. An analysis of the bright bands and streaky spots which appear in the dark-field images of the ropes has been made by observing the series of nanodiffraction patterns obtained as the incident beam is scanned slowly across the image of a rope. These results will be reported elsewhere, but it may be stated here that the image contrast may be interpreted in terms of the twisting and bending of the ropes and the occurrence of local defects in the lateral stacking of the nanotubes. Such defects may be associated with the changes of helix angle implied above or possibly with other types of modification of tube structure, or with inclusions or stacking faults.
Acknowledgements This research was supported by the Office of Naval Research (grant N0014-91-J1794 and order number N0014-95-F-0099), the Advanced Technology Program of the State of Texas (grant 003604-047) and the Robert A. Welch Foundation, and made use of the instrumentation of the Center for High Resolution Electron Microscopy at Arizona State University.
References [I] A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Pelit, J. Robert, C. Xu, Y.H. Lee, S.G. Kim, D.T. Colbert, G. Scuseria, D.
384
J.M. Cowley et aL / Chemical Physics Letters 265 (1997) 379-384
Tom{reek, J.R. Fischer and R.E. Smalley, Science 273 (1996) 483. [2] S. lijima and T. Ichihashi, Nature 363 (1993) 603. [3] C. Xu, D.T. Colbert, R.E. Smalley and G.E. Scuseria. in preparation. [4] N. Hamada, S. Sawada and A. Oshiyama, Phys. Rev. Lett., 68 (1992) 1579.
[5] J.M. Cowley, J. Electron Microsc. 45 (1996) 3. [6] J.M. Cowley, Ultramicroscopy 49 (1993) 4. [7] X.B. Zhang, X.F. Zhang, S. Amelinckx, G. Van Tenderloo, J Van Landuyt, Ultramicroscopy, 54 (1994) 237.